Elliptical polarization state

Note that if is a solution, then (f + n 2 is also a solution. From Equations (2.38) and (2.39) we have 

Because the light intensity does not change upon a transformation between two frames, a + b = AI + A, and thercfra-e 

The lengths of the principal semi-major axes can be calculated from the above two equations. The sense of the revolution of an elliptical polarization is determined by the sign of sin 5. If sin 0, the endpoint of the electric vector revolves clockwise (the light is coming toward the observer). If sin 5 0, the endpoint of the electric vector revolves counterclockwise. The ellipticity of the polarization ellipse is define by 

The positive sign is used for right-handed circular polarization while the negative sign is used for left-handed circular polarization. The ellipticity angle v is defined by 

We can also use the azimuthal angle, p, of the major axis and the eUipticity angle, v, to represent the polarization state. The values of (p and v of various polarization states are listed in Table 2.1. 

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The detailed compensation mechanism is explained using Figure 8.26(b). When the unpolarized light from backlight passes through the polarizer (point P), it becomes linearly polarized and its polarization state is located at point T, which deviates fi om the absorption axis of the analyzer (point A). Afterwards, the linearly polarized light (point T) traverses the positive a film, whose position on the Poincare sphere overlaps with point A, and its polarization state is rotated clockwise from point T to point E around the AO axis. Point E is the first intermediate elliptical polarization state. 

At other values of dAn, linearly polarized input light is changed to an elliptical polarization state. The major axis of the ellipse is rotated with respect to the input polarization. 

Polarization For plane-polarized (also called linearly polarized) photons, the plane within which the electric field vector oscillates can sit at any angle to a reference plane containing the wave vector, as shown in Figures 2A and 2B. Other polarization states are also possible in the right- and left-handed circular polarizations depicted in Figures 2C and 2D, the electric field vector sweeps out a helix about the direction of propagation. Elliptical polarization states are of an intermediate nature, between linear and circular. Together, the wave vector and polarization of a photon determine its mode. 

To describe a general state of polarization, we ascribe a phase shift 5 between the X and y components (see Chapter 6). Accordingly, the Jones vector for a general elliptical polarization state is of the form... 

Unfortunately, in the VUV region no polarimetry data are available, but calculations indicate the degree of circular polarization achieved by the wiggler may be 80%, estimated to be no worse than 70% delivered at the experimental chamber [95, 96]. In PECD experiments, we have calibrated the polarization state by deduction from cross-comparison of results at a few fixed energies previously studied on the SU5 beamline where accurate polarimetry data was available [36]. Because the horizontal magnetic field array in the insertion device is electromagnetic, fast current reversal to switch left- and right-handed elliptical polarizations is possible, with the usual potential benefit for dichroism measurements. 

In classical terms, radiation is represented by an electromagnetic wave. The polarization of plane-wave radiation is defined by the way the oscillating electric field evolves in space, in a plane perpendicular to the direction of propagation. The most general polarization state is called elliptical polarization [23], but for luminescence applications the subset of linear polarization states usually suffices. In these cases the electric field vector oscillates along a well defined direction in a plane perpendicular to the direction of propagation. This direction is the polarization direction, and radiation with this characteristic is said to be linearly polarized. 

All possible polarization states in (2.3) form the sphere of unit radius known as the Poincar0 sphere [33,10]. The longitude and latitude of a point on the sphere are respectively related to doubled azimuth 0 and ellipticity e of the polarization elhpse of the light. Polarizations, whose Stokes vectors form the matrices, can be represented by umnatched points on the Poincar0... 

Fig. 3. Energy level diagram illustrating S-type MCD. Two nondegenerate excited states, 1) and 12), are mixed by the external magnetic field, H. Transitions from the ground state of the system, 0), to the perturbed excited states, 1 ) and 2 ), are elliptically polarized in opposite senses.

The subcritical nature of the Freedericksz transition can be explained as follows. When the director settles to the precession state, light becomes el-liptically polarized inside the nematic. On the other hand, it is known that the Freedericksz transition for elliptically polarized light depends on ellipticity and... 

An ellipsometer measures the polarization state of light. Applied to electrode surfaces, monochromatic plane-polarized light is incident on the working electrode. The state of polarization of the reflected light is different it is in general elliptically... 

Although the emphasis in this section has been on linearly polarized incident radiation, considerable enhancement of the k-quantum photocurrent may occur for circularly (or elliptically) polarized radiation, as recently discussed by a number of authors [7.46]. We note that information relating to the intermediate-state lifetime of the detector (t,) can be obtained by measuring the two-quantum detector output for various values of t. ... 

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